About BfX

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Robert Meijer

What is BfX?

BfX is a tool for the sporting shooter who, from time to time, has to do some  calculations. BfX is accurate as long as the elevation is between -15 and + 15 degrees. This is typically the case for a target shooter. This restriction allows one to make the so called flat fire approximation which results in mathematical formulas for bullet trajectories and stateless algorithms.

A stateless algorithms does not keep information about the calculations done. Once the algoritm is finished, its memory is reset.  These algorithms are very suitable for the Excel context.

BfX is checked against models that do not apply this approximation, e.g. a 4th order Runge Kutta solver. The outcome of such comparisons is that if you stay below 15 degrees BfX works fine and is accurate enough. Enough means the following. If you do a calculation with BfX or a numerical solver for a trajectory to hit a target at 1000m that is right in front of you with a 740 m/s, .308 185grain Sierra Match King bullet the differences are less then the uncertainties due to the input of the calculations. How accurate does a chronograph measure the bullet speed? How well is the ballistic coefficient known? How well is the drag function measured? Near the velocity of sound?

Supporting the Runga Kutta or even the so called 6-degrees-of-freedom methods in Excel is certainly possible, yet unnecessary for competition shooting. The physics of BfX is explained in the book of Arthur Pejsa. There where quite a few typo’s and unnecessary approximations there, which found not their way into BfX. Pejsa supplies also a drag function that should be used with the G1 ballistic coefficient and this is the default drag function used in BfX. BfX also supports other drag functions, amongst which the G7 drag function. The G7 drag functions can be used in combination with the measured G7 (and G1) ballistic coefficients that you can take, for example, from the  book of Bryan Litz "Applied ballistics for longe range shooting". Furthermore, BfX contains a drag function termed "A" that is comparable with the one deployed by Chairgun Pro, a popular ballistics calculator of the airgun community.

BfX also supplies an interface to Visual Basic for Applications that is part of MS Word, Excel, Access etc. With this you can do your own programming.

Where can I get help?

Most explanation about the use of BfX is done in the workbooks you can download from this site. You might also consult other users via the forum. BfX itself provides help in Excel, use =BfX_Help(n) where n= empty, 0, 1, 2, ... 120. Look here fore an example. A list of =BfX_Help2(n) shows you all available units of physical quantities and lists available drag functions, have a look at  this page for an exampleBfX_Info() contains an optional range <r>, =BfX_Info(n,<r>) shows information on succesful or failed calculations and what is wrong with your use of BfX functions. It updates automatically if a cell in the range <r> has changed its value. =BfX_IQ(<r>) reports on the the last calculation.
Part of the workbook deployed by the author. Excel becomes with BfX a "ballistics workbench" calculating quantities one needs, read more ... A table with points of impact, created for a fellow shooter, see details ...
A section from the "getting started" workbook demonstrating the practical (lack of) effects of various drag functions, read more ... With BfX one can study the effects of drag functions, BfX contains very precise descriptions of the most frequently used ones, see details ...
BfX supports use by Excel macro programs, also  known als VBA programs, read more ... In principle one could even use BfX from Word and Powerpoint. Example of a regular ballistic calculator created in Excels VBA development environment, read more ...